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I have worked out I need to get a tram from Lyon Airport and go to either Lyon Perrache or Lyon Part Dieu and get a train from there. The site http://uk.voyages-sncf.com/ indicates that I can get to Paray Le Monial from Lyon in around 2 hours which is fine, but I am looking to confirm that it is a direct route as http://uk.voyages-sncf.com/ seems to indicate that I would not need to change stations.

This maybe too late but a few trains are direct. We have often caught the train from Lyon Part Dieu to La Clayette which is the stop before Paray. You can easily see direct trains if you look at the german website www,bahn,com which shows all trains and connections but you need to book on SNCF. We have never been able to reserve a seat and it can be busy so you may need to walk up and down the train to get seats together.